History is about understanding past events, not a place for polemic. There's another place and time for that, and it's called "propaganda" (by politicians). For those who tries to appreciate history, however uncomfortable the process might be, its benefits far outweighs the cost because history helps us learn how we got here, the 21st century. I believe this is the commonwealth we all want in a fairer, better world.
"Mongols, having already conquered half of Europe, decided the other half wasn't worth it"
Let me just say from the outset, of course this statement is not just arrogant and presumptuous, it is also silly for any modern historian to consider this question seriously if it were phrased precisely this way.
First, Frankish knights were not paper soldiers, the Crusades showed that. Any attack on the West is not cost-free. I will make a point about evaluation of "worth it" at the very end (below).
Second, this statement is a literary device for dramatic effect.
Finally, for those who truly want to understand the statement and how it might apply to the Mongol Empire, the details include not only facts about warfare (one damn fight after another), political leadership (the key players), their culture (which might help frame their intention), and, not least, the state of affairs in south-west Asia (Middle East) and eastern Europe.
Mongol Rulers (1206-1260 BCE) and the Final Ultimatum of 1261
Diagram: Qaghans (Great Khans) shown in bold (source).
Ultimatum of 1261
Only with detailed knowledge can we reasonably understand the events the Mongols undertook with regards their desire to invade the Latin west. By Peter Jackson, The Mongols and Europe:
These struggles marked the dissolution of the Mongol empire into four regional khanates: the Golden Horde in the west, which traditionally enjoyed a good deal of autonomy; the khanate of Chaghadai in central Asia, ruled by the progeny of Chinggis Khan’s second son; the state founded by Hülegü in Persia and ruled by his descendants, the so-called Il-khans; and the dominions of the qaghan in China and Mongolia, under Qubilai, who emerged victorious from his struggle with Arigh Böke in 1264. But even after his triumph, Qubilai, who abandoned Qaraqorum to reside in China, was recognised only by Hülegü and his successors, to whom he was more closely bound by ties of blood. From 1269, moreover, he was confronted in central Asia by another anti-qaghan, Ögödei’s grandson Qaidu (d. 1303). The Mongol world did not acknowledge a single emperor again until 1304.
The Mongol campaigns of 1259-60 in eastern Europe and in Syria were therefore the last military efforts of the united empire: significantly,the ultimatum received by Louis IX of France in 1261 (from Berke in all probability) is the latest recorded in western sources. The outbreak of hostilities in the Caucasus meant that neither the Il-khan nor the Khan of the Golden Horde was able to give his external frontiers single-minded attention. Now, moreover, for the first time, Mongol princes were ready to ally with foreign powers against fellow Mongols. From 1261-2 the Muslim Berke was engaged in reaching an understanding with his co-religionists the Mamluks, who were Hülegü’s chief external enemies and whose Qipchaq origin gave them a common ethnic back- ground with the majority of his own nomadic subjects.
Source: The New Cambridge Medieval History, Part VI - The Northern and Eastern Frontiers, Cambridge, 1999, p.710.
From Jackson's passages, it should be obvious Berke's ultimatum of 1261 for Louis IX raises three crucial points:
- William of Rubruck's exploration of Central Asia was no coincidence. He was sent by Louis IX. Rubruck's report gave the Latin west (some) insight into the Mongol Empire. Today, it's considered a "masterpiece of medieval geographical literature".
- Berke, successor of Batu Khan -- in 1261 alone, he gave an ultimatum to Latin west, whilst also negotiating on an alliance with the Mamluks because of his Islamic conversion. Was he solidifying his position (that of the Golden Horde) or was he really prepared to attack the west?
- Did Louis IX take Berke seriously, given that he knew the qaghan was Möngke? More pertinent, was the 1261 ultimatum from Möngke, or was it Berke's?
(point 3: There was no qaghan in 1261, because Möngke passed away suddenly in 1259, whilst Kublai's throne was not yet secure -- Toluid civil war, 1260–1264. Did Louis IX know this? Was he that up-to-date?)
(Please keep the last question in mind as you read the points raised below)
A Useful Answer?
Having said this, and how tediously long a reasonable answer should be (in my comments to OP, above), I will try to do so (hopefully, Central Asia specialists and Chinggisid-scholars will not flinch).
Let me start with a simple note: Mongol's relation and experience with China is of a totally different nature with that of Latin west.
To my knowledge, there is no direct evidence of any decision made regarding campaigns into Western Europe, post-Ögedei. All other evidence of any decision to invade the West was not made at the level of the Emperor, the Qaghan. As the direct successor of Chinggis, he had the authority to do so. Ögedei's general into the western sector was Eljigidei.
All other khans post-Ögedei did not possess such authority, therefore, also did not have at hand the necessary military resources.
This is a crucial point, because when united, the Mongols (with a lot of help from other Central Asian tribes & confederations, especially the Turks) were unprecedented military conquerors. Recall how the Huns (& other barbarians) brought the Roman Empire to its knees, starting with Battle of Adrianople (378 CE). Compared with the Huns who were based in the western steppe, Chinggis Khan united the entire Central Asia, the resources available to him was of a totally different scale. Pax Mongolica is not a figment of our imagination.
Ögedei's passing in 1241 put paid to any idea of further expanding west, all other successors -- Güyük, Möngke, and even the founder of the Yuan Dynasty, Kublai -- cannot/should not be considered qaghan, with entire resources of the Mongol Empire and political support for further expansion into the West.
Möngke was enthroned in 1251, by a quriltai, which also directed Hülegü to extend Mongol control into Iran and Iraq (not the Latin west). By this stage, the Mongol Empire was not as united as it once was. The evidence: Hülegü's protracted trip to Iran and Iraq. He left in 1253 (Ked Buqa, his advanced guard general left a year earlier). He finally arrived at Alamut Castle in 1256.
From decision to invasion, this is a 5-year gap. The delay was due to time required for raising necessary manpower & settling logistical needs (according to Allsen). However we look at it, Hülegü's campaign was not up to the normal standard of Mongol warfare & mobility.
For those familiar with Subedei, the acclaimed general of Chinggis khan with countless campaign experience who served the Empire so well - is this the modus operandi of the Mongols? Why didn't Batu Khan (d. 1255) of the Golden Horde lead/assist directly, since all he needed to do was attack south into the Caucasus, to help Hülegü and his qaghan, Möngke? No recce required, Mongols were there just two decades earlier, led by Subedei.
Which bring us to, whilst Hülegü was still campaigning in Iraq (Iran was achieved), Möngke passed in August 1259, on his campaign against China (Song). Kublai was also there, conducting a flanking movement in Yunnan, China.
3. A Question
To end, on whether it was worth it, allow me to ask: Why would the Mongols want to invade the Latin west, once trade relation was established? In context, given the west did not support the Mamluks, i.e. the Crusades. (Mongols were brilliant warriors and even better strategists, imho).
In fact, a better question is: Why didn't the Franco-Mongol alliance work out?
My comments on Great Wall of China
From Beckwith, Empires of the Silk Road, Princeton, 2011, p. 27 (additional links and emphasis mine):
In the east much of the best pastureland had been captured by Chinese invasions beginning in the Warring States period. The territory was held by Chinese fortresses and walls built right through the steppe, including the Great Wall, which mainly connected earlier walls together and strengthened them. These walls were not built to protect the Chinese from the Central Eurasians but to hold Central Eurasian territory conquered by the Chinese (Di Cosmo 2002a: 149–158). That is, they were offensive works, not defensive ones. The purpose of the nomadic raids or warfare against the Chinese was undoubtedly mainly to remove the Chinese from the seized pastureland and restore it to nomadic control, as indicated by the fact that the nomads almost exclusively took animals and people as booty on these raids (cf. Hayashi 1984). The theories ultimately based on the idea of the Chinese as victims of Central Eurasian aggression, and the nomads as poverty-stricken barbarians greedy for Chinese silks and other products, are not only unsupported by the Chinese historical sources, they are directly contradicted by them, as well as by archaeology. The same applies all along the frontier between Central Eurasia and the periphery of Eurasia, from east to west.
(If not useful, I hope it has been fun!)